Problem: Simplify the following expression: $q = \dfrac{p^2 + p - 56}{p + 8} $
Solution: First factor the polynomial in the numerator. $ p^2 + p - 56 = (p + 8)(p - 7) $ So we can rewrite the expression as: $q = \dfrac{(p + 8)(p - 7)}{p + 8} $ We can divide the numerator and denominator by $(p + 8)$ on condition that $p \neq -8$ Therefore $q = p - 7; p \neq -8$